CE3L-HW3

CIV ENG 3L03: Homework Assignment #3 (Due: 11:55pm on April 6) 1. (10%) (a) Sketch the molecular structure of EDTA. Indicate the ligands in the sketch. (b) Briefly explain how EDTA has strong affinity to heavy metal ions. (c) Do internet research regarding where EDTA is used and briefly write about your search results. (d) For the given chelating reaction, find the effective EDTA dose in M (mole/L) to reduce [Pb 2+ ] below 10 -10 M. Assume that the initial [Pb 2+ ] is 2 × 10 -4 M. EDTA 4- + Pb 2+ ↔ Pb-EDTA 2- K = 10 20 2. (15%) (a) Write the definition of reduction and oxidation. (b) Ammonia oxidizing bacteria (AOB) are one of important microorganisms in biological wastewater treatment. They oxidize ammonia (NH 3 ) and reduce O 2 into water. Balance the reduction and oxidation reactions driven by AOB. Assume that ammonia is oxidized to nitrite (NO 2 - ). (c) Combine the redox reactions into a single redox reaction. (d) Find ΔG° for the combined redox reaction. (e) Find ΔG for the given conditions: [NH 3 ] = 5 mM; [NO 2 - ] = 0.1 mM; [O 2 ] = 2.5 mg/L; pH = 7; and 25ºC. (f) Repeat Part (e) for pH 5. Discuss the effect of pH on the AOB activity. 3. (5%) (a) Determine the oxidation number of nitrogen in the following chemicals: N 2 ; NO 3 - , NO 2 - ; NH 3 . (b) Based on the changes in the oxidation number, determine whether the nitrification, denitrification, and fixation reactions are reduction or oxidation reactions. 4. (10%) (a) Find pKa 1 for the following acid dissociation reaction at 25 ° C. Start your answer by writing the equation for K written with ΔG°. H 2 CO 3 * ↔ HCO 3 - + H + Is your calculated pKa 1 value consistent with the value in the course handout? (b) Find pKa 1 for 15 and 35 ° C. Discuss how temperature affects the fractionation between bicarbonate and carbonic acid. 5. (10%) (a) Derive the equation for effluent tracer concentration from a CFSTR. Assume a step-input tracer test. Start your derivation by writing the mass balance equation and show detailed steps of derivation. (b) Repeat Part (a) for a spike input. 6. (15%) (a) Derive the equation for the effluent concentration from a CFSTR with a 1st-order decay reaction. Assume steady state and that the contaminant chemical is removed in the chemical reaction. Start your answer by writing the mass balance equation. Write the final equation with C in , τ , and k 0 (not with Q or V even though you have Q and V in the derivation). (b) Repeat Part (a) for a PFR that has a length of L . Start your answer by defining a control volume and writing the mass balance equation. Note that you are to derive the equation for effluent concentration (at x = L ). Write the final equation as a function of C in , τ , and k 0 (not with v , A, Q, L ). (c) Using your answers in Parts (a) and (b), plot the effluent concentration from CFSTR and PFR vs. the mean hydraulic retention time ( τ ) up to 60 min. Assume: C in = 150 mg/L; k 1 = 0.25 min -1 . What is the minimum retention time for 90% removal? Discuss which reactor is more efficient in removing the contaminant between CFSTR and PFR. 7. (15%) (a) Derive the following flux equation in gas transfer according to the two film theory. Write the name and dimension (i.e., unit) of each of kinetic and equilibrium constants in the equation. ࠵? = ࠵? ! ࠵? " ࠵? " + ࠵? ! ࠵? # (࠵? $ − ࠵? % ) Start your answer by sketching the interface between the gaseous and liquid phases and two adjacent films, and defining c I , c B , p B , and p I . Make sure to write necessary assumption(s). (b) Write the overall resistance, liquid film resistance, and gas film resistance for gas transfer. (c) For oxygen transfer, explain why the gas film resistance is negligible. (d) In biological wastewater treatment, we have aeration systems (air diffusers) to provide oxygen for microbial growth. Determine the rate of oxygen transfer in kg-O 2 /hr for the following treatment conditions: DO = 1.9 mg-O 2 /L; K H = 0.00145 M/atm; D O2 = 2.0 × 10 -5 cm 2 /s; δ L = 25 µm; a = 2500 m 2 /m 3 ; and volume of the reactor = 20,000 m 3 .